Reinvestigating the R2 Indicator: Achieving Pareto Compliance by Integration
Research output: Contribution to book/Conference proceedings/Anthology/Report › Conference contribution › Contributed › peer-review
Contributors
Abstract
In multi-objective optimization, set-based quality indicators are a cornerstone of benchmarking and performance assessment. They capture the quality of a set of trade-off solutions by reducing it to a scalar number. One of the most commonly used set-based metrics is the R2 indicator, which describes the expected utility of a solution set to a decision-maker under a distribution of utility functions. Typically, this indicator is applied by discretizing this distribution of utility functions, yielding a weakly Pareto-compliant indicator. In consequence, adding a nondominated or dominating solution to a solution set may – but does not have to – improve the indicator’s value. In this paper, we reinvestigate the R2 indicator under the premise that we have a continuous, uniform distribution of (Tchebycheff) utility functions. We analyze its properties in detail, demonstrating that this continuous variant is indeed Pareto-compliant – that is, any beneficial solution will improve the metric’s value. Additionally, we provide an efficient computational procedure to compute this metric for bi-objective problems in O(NlogN). As a result, this work contributes to the state-of-the-art Pareto-compliant unary performance metrics, such as the hypervolume indicator, offering an efficient and promising alternative.
Details
Original language | English |
---|---|
Title of host publication | Parallel Problem Solving from Nature – PPSN XVIII |
Editors | Michael Affenzeller, Stephan M. Winkler, Anna V. Kononova, Thomas Bäck, Heike Trautmann, Tea Tušar, Penousal Machado |
Pages | 202-216 |
Number of pages | 15 |
ISBN (electronic) | 978-3-031-70085-9 |
Publication status | Published - 7 Sept 2024 |
Peer-reviewed | Yes |
Publication series
Series | Lecture Notes in Computer Science |
---|---|
Volume | 15151 |
ISSN | 0302-9743 |
External IDs
Scopus | 85204641244 |
---|---|
ORCID | /0000-0003-3929-7465/work/168718802 |
ORCID | /0000-0003-2862-1418/work/168719590 |
Keywords
ASJC Scopus subject areas
Keywords
- Benchmarking, Multi-objective optimization, Pareto compliance, Performance assessment, R2 indicator, Utility functions